Engineering Calculus Notes 86

Engineering Calculus Notes 86 - 74 CHAPTER 1. COORDINATES...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 74 CHAPTER 1. COORDINATES AND VECTORS upward diagonal. We denote the determinant by replacing the brackets surrounding the array with vertical bars: 13 vextendsingle vextendsingle vextendsingle vextendsingle x 1 y 1 x 2 y 2 vextendsingle vextendsingle vextendsingle vextendsingle = x 1 y 2 − x 2 y 1 . It is also convenient to sometimes treat the determinant as a function of its rows, which we think of as vectors: −→ v i = x i −→ ı + y i −→ , i = 1 , 2; treated this way, the determinant will be denoted Δ( −→ v 1 , −→ v 2 ) = vextendsingle vextendsingle vextendsingle vextendsingle x 1 y 1 x 2 y 2 vextendsingle vextendsingle vextendsingle vextendsingle . If we are simply given the coordinates of the vertices of a triangle in the plane, without a picture of the triangle, we can pick one of the vertices—call it A —and calculate the vectors to the other two vertices—call them B and C —and then take half the determinant. This will equal the area of the triangle...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online